Transcript Formulating Statistical Questions and Collecting Data

Formulating Statistical Questions
and Collecting Data
Alliance Class
September 2011
GAISE: Instructional programs from
Pre K-12 should enable all students to:
1. Formulate questions that can be addressed
with data
2. Collect, organize, and display data
3. Analyze data
4. Interpret results
Definition of Statistical Questions
Statistical questions specify populations and
measurements of interest and anticipate
answers based on data that vary.
Common Core State Standards
Statistics & Probability 6.SP
Develop understanding of statistical variability.
1. Recognize a statistical question as one that
anticipates variability in the data related to the
question and accounts for it in the answers. For
example, “How old am I?” is not a statistical
question, but “How old are the students in my
school?” is a statistical question because one
anticipates variability in students’ ages.
Answers to statistical questions
• Address the variation in data
• Use probability statements
• Apply only to the population sampled
Non-Statistical questions may be very
broad or very specific
• Research Question:
• Does the pesticide Roundup harm ladybugs?
• Statistical Question:
• What is the mortality rate in Coccinella
transversalis on hour after treatment with a
5% solution of Roundup?
• Research question:
How has the WKCE math scores changed for our
school?
Statistical question:
Deterministic questions are very
specific.
• They anticipate fixed answers
• No randomness is involved
• Deterministic question: How tall is John?
• Statistical question: How tall are the students
in my class?
• Deterministic question: How many words are
there in this sentence?
• Statistical Question: How many words are
there in the sentences in this book?
Activity
• For each question listed on the handout
decide:
• Is it a statistical question or not?
• If it is not give a reason why not and rewrite
so that it is a statistical question
Types of Statistical Studies
How Data is Collected
GAISE Step Two
Designing a plan to collect appropriate data
Types of Variables
Experiments
Observational Studies
Surveys
Do you know who my favorite
horse is?
Not Seabiscuit
Not Trigger – the smartest horse in
Hollywood
Not Mr. Ed
Clever Hans the Math Horse
In the late 1800’s, a German Math teacher
named Wilhelm von Osten believed that
humans had greatly underestimated the
intelligence of animals. To test his hypothesis,
he “tutored” his horse named Hans.
Hans learned to use his hoof to tap out numbers
written on a blackboard. Wilhelm would write
a “3” on the board and Hans would tap-taptap. Hans could repeat this for any number
under 10
Encouraged by this success Wilhelm would write
a basic arithmetic problem like 3 + 4 on the
board and Hans would tap 7 times.
Wilhelm took Hans all over Germany. Large
crowds came out and were not disappointed.
Hans success rate was 89%
Naturally there were skeptics. The German
board of education assembled a team of
scientists to test Hans without Wilhelm
present.
Hans was successful – the board said Hans
talents were real.
This still didn’t quiet the skeptics.
Another scientists decided to test Hans again
but under a more controlled setting.
Hans did very well when the scientist posed the
questions under normal situations but Hans
failed when the scientist posed questions
standing behind Hans.
The scientist discovered that Hans had no real
grasp of math but was very receptive to the
subtle, unconscious cues which the human
questioners gave. Hans was sensitive to
humans body language.
Researchers now have a term called “Clever
Hans Effect” that describes the influence of a
questioner’s subtle and unintentional cues
given when asking questions.
Types of Data
Quantitative Data
Takes numerical values for which arithmetic
operations such as averaging make sense
Continuous
Decimals and fractions
Height of a person
Discrete
Whole numbers
Number right on a test
Type of Data
Categorical or Qualitative Data
Places an individual into one of several groups
or categories
Favorite pizza toppings
Who you vote for
Ethnic background of your students
Clever Hans Variables
When the scientist tested Hans, what were
some of the variables that were tested and
not tested?
What type were these variables?
Vocabulary
Populations vs Samples
• Population
A population consists of all members of some
specified group.
• Sample
A sample is a subset of a population. It has the
same characteristics as the population.
Parameters vs Statistics
• Parameters
A measure of a characteristic of an entire
population.
• Statistic
A measure of a characteristic of a sample.
Designs for Collecting Data
• Experiments
• Observational Studies
Surveys
Experiments
• The researchers deliberately impose some
treatment on individuals and observe their
responses.
• Causation is best established by an
experiment
Examples of experiments
•
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•
Eating Chocolate
Breast Cancer
Velcro and Babies
McDonalds
Observational Studies
• Researchers observe individuals and measure
variables of interest but do not attempt to
influence the responses
• Association between variables may be
observed but not causation.
Examples of Observational Studies
• Breast Feeding
• Night Lights
Experiments vs Observational Studies
• Hormone Therapy Treatment Studies
Surveys
• An important type of observational study
• Surveys may be given to a sample from the
population of interest
• Or they may be given to the entire population
and referred to as a CENSUS
Activity
• For each study try and answer the following
questions:
• What is the statistical question?
• Is the study an experiment or observational
study?
• What is the population of interest?
• What is the result or conclusion of the study?
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Electrical Brain Simulation
Math Whizzes
Hands-on math
Three cell phone studies
Sleep apnea
Principles of Experimental Design
• Randomization
Random assignment of treatment
• Repetition
Repeat the experiment to a “large” number of subjects
• Control
Compare two or more treatments to prevent
confounding
Placebo
Randomized Comparative Design
Does taking Vitamin C reduce the occurrence of the flu?
808 student volunteers who had not gotten a flu shot
were randomly assigned to one of two groups: a
treatment group who received 1000 mg vitamin C daily
and a control group who received a placebo. All the
students where monitored daily to ensure they
adhered to their assigned treatment. At the end of the
school year all the student’s medical records were
examined to determine if they had contracted the flu.
Cell Phone Study
Show the design of the Stewart Fist experiment
Tai Chi or Yoga?
Read the description of the study done to
compare Tai Chi and Yoga.
Answer the questions